UV Completion Research Articles

Toward a UV model of kinetic mixing and portal matter. II. Exploring unification in an SU(N) group

If dark matter interacts with the Standard Model (SM) via the $U(1{)}_{D}$ kinetic mixing portal at low energies, it necessitates not only the existence of portal matter particles which carry both dark and SM quantum numbers, but also a possible UV completion into which this $U(1{)}_{D}$ and the SM are both embedded. In earlier work, following a bottom-up approach, we attempted to construct a more unified framework of these SM and dark sector interactions. In this paper, we will instead begin to explore, from the top down, the possibility of the unification of these forces via the decomposition of a grand-unified-theory-like group, $G\ensuremath{\rightarrow}{G}_{\mathrm{SM}}\ifmmode\times\else\texttimes\fi{}{G}_{\mathrm{Dark}}$, where $U(1{)}_{D}$ is now a low-energy diagonal subgroup of ${G}_{\mathrm{Dark}}$ and where the familiar ${G}_{\mathrm{SM}}=SU(5)$ will play the role of a proxy for the conventional $SU(3{)}_{c}\ifmmode\times\else\texttimes\fi{}SU(2{)}_{L}\ifmmode\times\else\texttimes\fi{}U(1{)}_{Y}$ SM gauge group. In particular, for this study it will be assumed that $G=SU(N)$ with $N=6--10$. Although not our main goal, models that also unify the three SM generational structure within this same general framework will also be examined. The possibilities are found to be quite highly constrained by our chosen set of model-building requirements, which are likely too strong when they are employed simultaneously to obtain a successful model framework.

Are there Einsteinian gravities involving covariant derivatives of the Riemann tensor?

We study the particle content of higher derivative theories of gravity built with contractions of the Riemann tensor and its covariant derivatives. In the absence of the latter, there is a family of theories exhibiting an Einsteinian spectrum known as generalized quasi-topological gravities. In turn, we present a no-go result for the construction of Einsteinian gravities involving covariant derivatives of the Riemann tensor. We find evidences suggesting that (truncated series) finite order Lagrangians with covariant derivatives of the Riemann tensor generically present ghosts in their spectrum. This might be interpreted as a hint of non-locality in any healthy UV completion of General Relativity.

IR side of positivity bounds

We show how calculable IR loop effects impact positivity bounds in Effective Field Theories with causal and unitary UV completions. We identify infrared singularities which appear in dispersion relations at $|t|\lesssim m^2$. In the massless limit, they weaken two-sided bounds based on crossing symmetry, such as the lower bound on the amplitude for Galileon scattering. For amplitudes that are analytic in $s$ even for large negative $t$, i.e. $|t|\gg m^2$, we propose a new simple analytic approach to dispersive bounds, which are instead insensitive to the singularities, and explicitly compute the finite contributions from loops. Finally we show that the singularity do not affect the bounds based on smearing in impact parameter.

UV graviton scattering and positivity bounds from IR dispersion relations

Scattering amplitudes mediated by graviton exchange display IR singularities in the forward limit. This obstructs standard application of positivity bounds based on twice subtracted dispersion relations. Such divergences can be cancelled only if the UV limit of the scattering amplitude behaves in a specific way, which implies a very non-trivial connection between the UV and IR behaviors of the amplitude. We show that this relation can be expressed in terms of an integral transform, obtaining analytic results when $t \log{s}\rightarrow 0$. Carefully applying this limit to dispersion relations, we find that infinite arc integrals, which are usually taken to vanish, can give a non-trivial contribution in the presence of gravity, unlike in the case of finite negative $t$. This implies that gravitational positivity bounds cannot be trusted unless the size of this contribution is estimated in some way, which implies assumptions on the UV completion of gravitational interactions. We discuss the relevance of these findings in the particular case of QED coupled to gravity.

The well-posedness of the Cauchy problem for self-interacting vector fields

We point out that the initial-value (Cauchy) problem for self-interacting vector fields presents the same well-posedness issues as for first-order derivative self-interacting scalar fields (often referred to as k-essence). For the latter, suitable strategies have been employed in the last few years to successfully evolve the Cauchy problem at the level of the infrared theory, without the need for an explicit ultraviolet completion. We argue that the very same techniques can also be applied to self-interacting vector fields, avoiding a number of issues and “pathologies” recently found in the literature.

Implications of the muon anomalous magnetic moment for the LHC and MUonE

We consider the anomalous magnetic moment of the muon $a_\mu$, which shows a significant deviation from the Standard Model expectation given the recent measurements at Fermilab and BNL. We focus on Standard Model Effective Field Theory (SMEFT) with the aim to identify avenues for the upcoming LHC runs and future experiments such as MUonE. To this end, we include radiative effects to $a_\mu$ in SMEFT to connect the muon anomaly to potentially interesting searches at the LHC, specifically Higgs decays into muon pairs and such decays with resolved photons. Our investigation shows that similar to results for concrete UV extensions of the Standard Model, the Fermilab/BNL result can indicate strong coupling within the EFT framework and $a_\mu$ is increasingly sensitive to a single operator direction for high scale UV completions. In such cases, there is some complementarity between expected future experimental improvements, yet with considerable statistical challenges to match the precision provided by the recent $a_\mu$ measurement.

Dark energy star in gravity's rainbow

The concept of dark energy can be a candidate for preventing the gravitational collapse of compact objects to singularities. According to the usefulness of gravity's rainbow in UV completion of general relativity (by providing a new description of spacetime), it can be an excellent option to study the behavior of compact objects near phase transition regions. In this work, we obtain a modified Tolman-Openheimer-Volkof (TOV) equation for anisotropic dark energy as a fluid by solving the field equations in gravity's rainbow. Next, to compare the results with general relativity, we use a generalized Tolman-Matese-Whitman mass function to determine the physical quantities such as energy density, radial pressure, transverse pressure, gravity profile, and anisotropy factor of the dark energy star. We evaluate the junction condition and investigate the dynamical stability of dark energy star thin shell in gravity's rainbow. We also study the energy conditions for the interior region of this star. We show that the coefficients of gravity's rainbow can significantly affect this non-singular compact object and modify the model near the phase transition region.

Improved white dwarves constraints on inelastic dark matter and left-right symmetric models

WIMPs can be captured in compact stars such as white dwarves (WDs) leading to an increase in the star luminosity through their annihilation process. We show that when the WIMP interacts with the nuclear targets within the WD through inelastic scattering and its mass exceeds a few tens GeV the data on low-temperature large-mass WDs in the Messier 4 globular cluster can probe values of the mass splitting $\delta\lesssim$ 40 MeV. Such value largely exceeds those ensuing from direct detection and from solar neutrino searches. We apply such improved constraint to the specific DM scenario of a self-conjugate bi-doublet in the Left-Right Symmetric Model (LRSM), where the standard $SU(2)_L$ group with coupling $g_L$ is extended by an additional $SU(2)_R$ with coupling $g_R$. We show that bounds from WDs significantly reduce the cosmologically viable parameter space of such scenario, in particular requiring $g_R>g_L$. For instance, for $g_R/g_L$ = 1.8 we find the two viable mass ranges 1.2 TeV $\lesssim m_\chi\lesssim$ 3 TeV and 5 TeV $\lesssim m_\chi\lesssim$ 10 TeV, when the charged $SU(2)_R$ gauge boson mass $M_{W_2}$ is lighter than $\simeq$ 12 TeV. We also discuss the ultraviolet completion of the LRSM model, when the latter is embedded in a Grand Unified Theory. We show that such low-energy parameter space and compatibility to proton-decay bounds require a non-trivial extension of the particle content of the minimal model. We provide a specific example where $M_{W_2}\lesssim$ 10 TeV is achieved by extending the LRSM at high energy with color triplets that are singlets under all other groups, and $g_R/g_L>$1 is obtained by introducing $SU(2)_L$ triplets with no $SU(2)_R$ counterparts, i.e. by breaking the symmetry between the multiplets of $SU(2)_L$ and $SU(2)_R$.

Moments for positivity: using Drell-Yan data to test positivity bounds and reverse-engineer new physics

Moments of the leptonic angular distribution in the Drell-Yan process have recently been shown to be sensitive probes of a specific class of dimension-8, four-fermion operators in the Standard Model Effective Field Theory, involving a pair of quarks and leptons. The same operators are also subject to positivity bounds, when requiring the associated (unknown) UV completion to obey basic principles of quantum field theory. We perform a phenomenological study to quantify the sensitivity of the high-luminosity LHC to this set of operators and, by extension, the positivity bounds. We further extend the angular basis of moments and consider double differential information to improve the ability to disentangle the different operators, leading to a sensitivity to new physics scales up to 3 TeV. We use this information to explore the violation of positivity at the LHC as a way to test the underlying principles of quantum field theory. Finally, we present a case study which combines our results with information from other (current and prospective) experiments, as well as the positivity cone to infer the properties of possible tree-level UV completions. The data lead to robust, model-independent lower bounds on the M/sqrt{g} combination of the particle mass and coupling, for states that couple to right-handed leptons and/or up quarks.

Resolving the pathologies of self-interacting Proca fields: A case study of Proca stars

It has been argued that a self-interacting massive vector field is pathological due to a dynamical formation of a singular effective metric of the vector field, which is the onset of a gradient or ghost instability. We discuss that this singularity formation is not necessarily a fundamental problem but a breakdown of the effective field theory (EFT) description of the massive vector field. By using a model of ultraviolet (UV) completion of the massive vector field, we demonstrate that a Proca star, a self-gravitating condensate of the vector field, continues to exist even after the EFT suffers from a gradient instability without any pathology at UV, in which the EFT description is still valid and the gradient instability in EFT may be interpreted as a standard dynamical instability of a high-density boson star from the UV perspective. On the other hand, we find that the EFT description is broken before the ghost instability appears. This suggests that a heavy degree of freedom may be spontaneously excited to cure the pathology of the EFT as the EFT dynamically tends to approach the onset of the ghost instability.

Muon g−2 and a type-X two-Higgs-doublet scenario: Some studies in high-scale validity

We study the high-scale validity of a Type-X two Higgs doublet scenario which provides an explanation of the observed value of muon $(g-2)$. This region admits of a pseudoscalar physical state, which is well below the observed 125-GeV scalar in mass. A second neutral scalar particle can be both above and below 125 GeV in such a scenario. Admissible regions in the parameter space are obtained by using the most recent data on muon $(g-2)$, theoretical constraints such as low-scale perturbativity and vacuum stability, and also all experimental constraints, including the available LHC results. Among other things, both the aforesaid orders of CP-even neutral scalar masses are included in our benchmark studies. Two-loop renormalisation group equations are used to predict the values of various couplings at high scales, and the regions in the space spanned by low-scale parameters, which retain perturbative unitarity as well as vacuum stability upto various scales are identified. We thus conclude that such a scenario, while successfully explaining the observed muon $(g-2)$, can be valid upto energy scales ranging from $10^{4}$ GeV to the Planck scale, thus opening up directions of thought on its ultraviolet completion.

Loops, local corrections and warping in the LVS and other type IIB models

To establish metastable de Sitter vacua or even just scale-separated AdS, control over perturbative corrections to the string-derived leading-order 4d lagrangian is crucial. Such corrections can be classified in three types: first, there are genuine loop effects, insensitive to the UV completion of the 10d theory. Second, there are local α′ corrections or, equivalently, 10d higher-dimension operators which may or may not be related to loop-effects. Third, warping corrections affect the 4d Kahler potential but are expected not to violate the 4d no-scale structure. With this classification in mind, we attempt to derive the Berg-Haack-Pajer conjecture for Kahler corrections in type-IIB Calabi-Yau orientifolds and extend it to include further terms. This is crucial since the interesting applications of this conjecture are in the context of generic Calabi-Yau geometries rather than in the torus-based models from which the main motivation originally stems. As an important by-product, we resolve a known apparent inconsistency between the parametric behaviour of string loop results and field-theoretic expectations. Our findings lead to some interesting new statements concerning loop effects associated with blowup-cycles, loop corrections in fibre inflation, and possible logarithmic effects in the Kahler and scalar potential.

Integrating out beyond tree level and relativistic superfluids

We revisit certain subtleties of renormalization that arise when one derives a low-energy effective action by integrating out the heavy fields of a more complete theory. Usually these subtleties are circumvented by matching some physical observables, such as scattering amplitudes, but a more involved procedure is required if one is interested in deriving the effective theory to all orders in the light fields (but still to fixed order in the derivative expansion). As a concrete example, we study the U(1) Goldstone low-energy effective theory that describes the spontaneously broken phase of a ϕ4 theory for a complex scalar. Working to lowest order in the derivative expansion, but to all orders in the Goldstones, we integrate out the radial mode at one loop and express the low-energy effective action in terms of the renormalized couplings of the UV completion. This yields the one-loop equation of state for the superfluid phase of (complex) ϕ4. We perform the same analysis for a renormalizable scalar SO(N) theory at finite chemical potential, integrating out the gapped Goldstones as well, and confirm that the effective theory for the gapless Goldstone exhibits no obvious sign of the original SO(N) symmetry.

Spinning sum rules for the dimension-six SMEFT

We construct new dispersive sum rules for the effective field theory of the standard model at mass dimension six. These spinning sum rules encode information about the spin of UV states: the sign of the IR Wilson coefficients carries a memory of the dominant spin in the UV completion. The sum rules are constructed for operators containing scalars and fermions, although we consider the dimension-six SMEFT exhaustively, outlining why equivalent relations do not hold for the remaining operators. As with any dimension-six dispersive argument, our conclusions are contingent on the absence of potential poles at infinity — so-called boundary terms — and we discuss in detail where these are expected to appear. There are a number of phenomenological applications of spinning sum rules, and as an example we explore the connection to the Peskin-Takeuchi parameters and, more generally, the set of oblique parameters in universal theories.

Unitarization of infinite-range forces: graviton-graviton scattering

A method to unitarize the scattering amplitude produced by infinite-range forces is developed and applied to Born terms. In order to apply S-matrix techniques, based on unitarity and analyticity, we first derive an S-matrix free of infrared divergences. This is achieved by removing a divergent phase factor due to the interactions mediated by the massless particles in the crossed channels, a procedure that is related to previous formalisms to treat infrared divergences. We apply this method in detail by unitarizing the Born terms for graviton-graviton scattering in pure gravity and we find a scalar graviton-graviton resonance with vacuum quantum numbers (JPC = 0++) that we call the graviball. Remarkably, this resonance is located below the Planck mass but deep in the complex s-plane (with s the usual Mandelstam variable), so that its effects along the physical real s axis peak for values significantly lower than this scale. This implies that the corrections to the leading-order amplitude in the gravitational effective field theory are larger than expected from naive dimensional analysis for s around and above the peak position. We argue that the position and width of the graviball are reduced when including extra light fields in the theory. This could lead to phenomenological consequences in scenarios of quantum gravity with a large number of such fields or, in general, with a low-energy ultraviolet completion. We also apply this formalism to two non-relativistic potentials with exact known solutions for the scattering amplitudes: Coulomb scattering and an energy-dependent potential obtained from the Coulomb one with a zero at threshold. This latter case shares the same J = 0 partial-wave projected Born term as the graviton-graviton case, except for a global factor. We find that the relevant resonance structure of these examples is reproduced by our methods, which represents a strong indication of their robustness.

From conformal correlators to analytic S-matrices: CFT1/QFT2

We study families of one-dimensional CFTs relevant for describing gapped QFTs in AdS2. Using the Polyakov bootstrap as our main tool, we explain how S-matrices emerge from the flat space limit of CFT correlators. In this limit we prove that the CFT OPE density matches that of a generalized free field, and that this implies unitarity of the S-matrix. We establish a CFT dispersion formula for the S-matrix, proving its analyticity except for singularities on the real axis which we characterize in terms of the CFT data. In particular positivity of the OPE establishes that any such S-matrix must satisfy extended unitarity conditions. We also carefully prove that for physical kinematics the S-matrix may be more directly described by a phase shift formula. Our results crucially depend on the assumption of a certain gap in the spectrum of operators. We bootstrap perturbative AdS bubble, triangle and box diagrams and find that the presence of anomalous thresholds in S-matrices are precisely signaled by an unbounded OPE arising from violating this assumption. Finally we clarify the relation between unitarity saturating S-matrices and extremal CFTs, establish a mapping between the dual S-matrix and CFT bootstraps, and discuss how our results help understand UV completeness or lack thereof for specific S-matrices.

On the classification of UV completions of integrable Toverline{T} deformations of CFT

It is well understood that 2d conformal field theory (CFT) deformed by an irrelevant Toverline{T} perturbation of dimension 4 has universal properties. In particular, for the most interesting cases, the theory develops a singularity in the ultra-violet (UV), signifying a shortest possible distance, with a Hagedorn transition in applications to string theory. We show that by adding an infinite number of higher [ Toverline{T} ]s>1 irrelevant operators of positive integer scaling dimension 2(s+1) with tuned couplings, this singularity can be resolved and the theory becomes UV complete with a Virasoro central charge cUV> cIR consistent with the c-theorem. We propose an approach to classifying the possible UV completions of a given CFT perturbed by [ Toverline{T} ]s that are integrable. The main tool utilized is the thermodynamic Bethe ansatz. We study this classification for theories with scalar (diagonal) factorizable S-matrices. For the Ising model with cIR = frac{1}{2} we find 3 UV completions based on a single massless Majorana fermion description with cUV = frac{7}{10} and frac{3}{2} , which both have mathcal{N} = 1 SUSY and were previously known, and we argue that these are the only solutions to our classification problem based on this spectrum of particles. We find 3 additional ones with a spectrum of 8 massless particles related to the Lie group E8 appropriate to a magnetic perturbation with cUV = frac{21}{22},frac{15}{12} , and frac{31}{2} . We argue that it is likely there are more cases for this E8 spectrum. We also study simpler cases based on su(3) and su(4) where we can propose complete classifications. For su(3) the infrared (IR) theory is the 3-state Potts model with cIR = frac{4}{5} and we find 3 completions with frac{4}{5} < cUV≤ frac{16}{5} . For the su(4) case, which has 3 particles and cIR = 1, and we find 11 UV completions with 1 < cUV ≤ 5, most of which were previously unknown.

Causality constraints on black holes beyond GR

We derive causality constraints on the simplest scalar-tensor theories in which black holes differ from what General Relativity predicts, a scalar coupled to the Gauss-Bonnet or the Chern-Simons terms. Demanding that time advances are unobservable within the regime of validity of these effective field theories, we find their cutoff must be parametrically of the same size as the inverse Schwarzschild radius of the black holes for which the non-standard effects are of order one. For astrophysical black holes within the range of current gravitational wave detectors, this means a cutoff length of the order of kilometers. We further explore the leading additional higher-dimensional operators potentially associated with the scale of UV completion and discuss their phenomenological implications for gravitational wave science.

Well-posed UV completion for simulating scalar Galileons

The Galileon scalar field theory is a prototypical example of an effective field theory that exhibits the Vainshtein screening mechanism, which is incorporated into many extensions to Einstein gravity. The Galileon describes the helicity zero mode of gravitational radiation, the presence of which has significant implications for predictions of gravitational waves from orbiting objects, and for tests of gravity sensitive to additional polarizations. Because of the derivative nature of their interactions, Galileons are superficially not well-posed as effective field theories. Although this property is properly understood merely as an artifact of the effective field theory truncation, and is not theoretically worrisome, at the practical level it nevertheless renders numerical simulation highly problematic. Notwithstanding, previous numerical approaches have successfully evolved the system for reasonable initial data by slowly turning on the interactions. We present here two alternative approaches to improving numerical stability in Galileon numerical simulations. One of these is a minor modification of previous approaches, which introduces a low pass filter that amounts to imposing a UV cutoff together with a relaxation method of turning on interactions. The second approach amounts to constructing a (numerical) UV completion for which the dynamics of the high momentum modes is under control, and for which it is unnecessary to slowly turn on nonlinear interactions. We show that numerical simulations of the UV theory successfully reproduce the correct Galileon dynamics at low energies, consistent with the low-pass filter method and with previous numerical simulations.

Sterile neutrino portals to Majorana dark matter: effective operators and UV completions

Stringent constraints on the interactions of dark matter with the Standard Model suggest that dark matter does not take part in gauge interactions. In this regard, the possibility of communicating between the visible and dark sectors via gauge singlets seems rather natural. We consider a framework where the dark matter talks to the Standard Model through its coupling to sterile neutrinos, which generate active neutrino masses. We focus on the case of Majorana dark matter, with its relic abundance set by thermal freeze-out through annihilations into sterile neutrinos. We use an effective field theory approach to study the possible sterile neutrino portals to dark matter. We find that both lepton-number-conserving and lepton-number-violating operators are possible, yielding an interesting connection with the Dirac/Majorana character of active neutrinos. In a second step, we open the different operators and outline the possible renormalisable models. We analyse the phenomenology of the most promising ones, including a particular case in which the Majorana mass of the sterile neutrinos is generated radiatively.